If the sum of the circumferences of two circles with radii \(R_1\) and \(R_2\) is equal to the circumference of a circle of radius \(R\), then
\(R_1 + R_2 = R\)
\(R_1 + R_2 > R\)
\(R_1 + R_2 < R\)
Nothing definite can be said about the relation among \(R_1, R_2\) and \(R\).
Step 1: Recall the formula for the circumference of a circle. Circumference (C) = \(2 \pi r\), where \(r\) is the radius (measured in metres, SI unit).
Step 2: For the first circle with radius \(R_1\), circumference = \(2 \pi R_1\).
Step 3: For the second circle with radius \(R_2\), circumference = \(2 \pi R_2\).
Step 4: The problem says the sum of these two circumferences is equal to the circumference of another circle with radius \(R\). So, \[ 2\pi R_1 + 2\pi R_2 = 2\pi R \]
Step 5: Take \(2 \pi\) common on the left side: \[ 2\pi (R_1 + R_2) = 2\pi R \]
Step 6: Cancel \(2 \pi\) from both sides (since \(2 \pi \neq 0\)): \[ R_1 + R_2 = R \]
Final Answer: The sum of the radii of the two circles is equal to the radius of the third circle. Hence, option (A) is correct.